Question

The percentage profit earned by selling an article for Rs. 1920 is equal to the percentage loss incurred by selling the same article for Rs. 1280. At what price should the article be sold to make 25% profit?

Answer 1

Hint: - The selling price is the price at which a product is actually sold. The cost price is the price at which a product is bought.
The formula for finding x percentage of any quantity 1 is
\[\dfrac{x}{100}\times Quantity\ 1\]
The formula for calculating the profit or loss % for a product is as follows
 \[\left( profit/loss \right)\%=\dfrac{\left( profit/loss \right)}{\cos t\ price}\times 100\]

Complete step-by-step answer:

As per the question, the percentage profit earned by selling an article for Rs. 1920 is equal to the percentage loss incurred by selling the same article for Rs. 1280.
Let the cost price of the product be Rs. x. As the product sold at Rs.1920, therefore, the selling price of the product is Rs. 1920. Let p be the profit% that is when the product is sold at Rs. 1920. So,
\[p=\dfrac{1920-x}{x}\times 100\ \ \ \ \ ...(a)\]
Now, this value of p is equal to the loss% which is when the product is sold at Rs.1280. So, we can write as
  \[p=\dfrac{x-1280}{x}\times 100\]
Now, we can use the value of p from equation (a) and so, we can write the following as follows
\[\begin{align}
  & \dfrac{1920-x}{x}\times 100=\dfrac{x-1280}{x}\times 100 \\
 & 1920-x=x-1280 \\
 & 2x=3200 \\
 & x=1600 \\
\end{align}\]
Hence, the cost price of the product is Rs. 1600.
Now, we have to find the selling price to make a profit of 25%, hence, we can write as
\[\begin{align}
  & 25=\dfrac{x-1600}{1600}\times 100 \\
 & x-1600=400 \\
 & x=2000 \\
\end{align}\]
Hence, for making a profit of 25%, the selling price of the product should be Rs. 2000.

Note: -The students can make an error if they don’t know about the formula which is given in the hint as
The formula for calculating the profit or loss % for a product is as follows
\[\begin{align}
  & \left( profit \right)\%=\dfrac{selling\ price-\cos t\ price}{\cos t\ price}\times 100 \\
 & \left( loss \right)\%=\dfrac{\cos t\ price-selling\ price}{\cos t\ price}\times 100 \\
\end{align}\]
This is a very important formula and not knowing this can land the student into deep trouble.